Subgroups — #15768805

Order 3328.

822 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88059	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718767	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718115	C₂	1	2	yes	maximal
4	#13114532	C₂	1	2	yes	maximal
5	C₂²×C₄×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×#88180	C₂²	1	2	yes	—
10	C₂²×#6099	C₂²	1	2	yes	—
11	C₂×C₄×C₈×C₁₃	—	2	2	no	—
12	C₂×C₄×C₈×C₁₃	—	2	2	no	—
13	C₂×C₄×C₈×C₁₃	C₄	1	4	yes	complemented
14	C₂×#88059	—	2	2	no	—
15	C₂×#88059	—	2	2	no	—
16	C₂×#88059	C₄	1	4	yes	complemented
17	#11718767	—	2	2	no	—
18	#11718767	—	2	2	no	—
19	C₂×#88058	C₄	1	2	yes	complemented
20	C₂×#88057	C₄	1	2	yes	complemented
21	#11718142	—	2	4	no	—
22	#11718115	—	2	4	no	—
23	C₂³×C₄×C₁₃	—	2	1	no	—
24	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
25	C₂²×C₈×C₁₃	—	2	1	no	—
26	C₂²×C₈×C₁₃	—	2	1	no	—
27	C₂²×C₈×C₁₃	—	2	1	no	—
28	C₂²×C₈×C₁₃	—	2	1	no	—
29	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
32	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
33	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
34	C₂²×C₈×C₁₃	D₄	1	2	yes	—
35	C₂²×C₈×C₁₃	D₄	1	2	yes	—
36	C₂²×C₈×C₁₃	D₄	1	2	yes	—
37	C₂²×C₈×C₁₃	D₄	1	2	yes	—
38	C₂²×C₈×C₁₃	Q₈	1	2	yes	—
39	C₂²×C₈×C₁₃	Q₈	1	2	yes	—
40	C₂×C₄²×C₁₃	—	2	1	no	—
41	C₂×C₄²×C₁₃	—	2	1	no	—
42	C₂×C₄²×C₁₃	—	2	1	no	—
43	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
44	C₂×C₄²×C₁₃	D₄	1	2	yes	—
45	C₂×C₄²×C₁₃	Q₈	1	2	yes	—
46	C₂×C₂²⋊Dic₁₃	—	2	2	no	—
47	#88180	—	2	2	no	—
48	#88180	—	2	2	no	—
49	#88180	—	2	2	no	—
50	#88180	—	2	2	no	—
51	C₂×C₄⋊Dic₁₃	C₂×C₄	1	4	yes	—
52	C₂×C₄×Dic₁₃	—	2	2	no	—
53	C₂×#6099	—	2	2	no	—
54	C₂×#6099	—	2	2	no	—
55	C₂×#6099	—	2	2	no	—
56	C₂×#6099	—	2	2	no	—
57	C₂×#6099	—	2	2	no	—
58	C₂×#6099	C₂×C₄	1	4	yes	—
59	C₂²×#1055	—	2	2	no	—
60	C₄×C₈×C₁₃	—	2	8	no	—
61	#88059	—	2	8	no	—
62	#88058	—	2	4	no	—
63	#88057	—	2	4	no	—
64	#10859	—	13	1	no	maximal, Sylow
65	C₂⁴×C₁₃	#41	1	1	yes	characteristic
66	C₂²×C₄×C₁₃	—	2	8	no	—
67	C₂²×C₄×C₁₃	—	2	2	no	—
68	C₂²×C₄×C₁₃	—	2	2	no	—
69	C₂²×C₄×C₁₃	—	2	2	no	—
70	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
79	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
80	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
81	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
82	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
83	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
84	C₂²×Dic₁₃	—	2	4	no	—
85	C₂×C₈×C₁₃	—	2	2	no	—
86	C₂×C₈×C₁₃	—	2	2	no	—
87	C₂×C₈×C₁₃	—	2	2	no	—
88	C₂×C₈×C₁₃	—	2	2	no	—
89	C₂×C₈×C₁₃	—	2	2	no	—
90	C₂×C₈×C₁₃	—	2	2	no	—
91	C₂×C₈×C₁₃	C₄²	1	2	yes	—
92	C₂×C₈×C₁₃	C₄²	1	2	yes	—
93	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
94	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
95	C₂×C₈×C₁₃	C₂²⋊C₄	1	4	yes	—
96	C₂×C₈×C₁₃	C₂²⋊C₄	1	4	yes	—
97	C₂×C₈×C₁₃	C₄⋊C₄	1	4	yes	—
98	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
99	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
100	C₂×C₈×C₁₃	C₄⋊C₄	1	4	yes	—
101	C₂×C₈×C₁₃	C₄⋊C₄	1	4	yes	—
102	C₄²×C₁₃	—	2	2	no	—
103	C₄²×C₁₃	—	2	2	no	—
104	C₄²×C₁₃	—	2	2	no	—
105	C₄²×C₁₃	C₄⋊C₄	1	4	yes	—
106	C₂²⋊Dic₁₃	—	4	2	no	—
107	C₂²⋊Dic₁₃	—	4	2	no	—
108	C₄⋊Dic₁₃	—	2	4	no	—
109	C₄⋊Dic₁₃	—	2	4	no	—
110	C₄×Dic₁₃	—	4	2	no	—
111	C₄×Dic₁₃	—	4	2	no	—
112	#6099	—	2	4	no	—
113	#6099	—	2	4	no	—
114	#6099	—	4	2	no	—
115	#6099	—	4	2	no	—
116	C₂×#1055	—	2	4	no	—
117	C₂×#1055	—	4	2	no	—
118	C₂×#1055	—	4	2	no	—
119	C₂²×#108	—	13	1	no	—
120	C₂×#427	—	13	1	no	—
121	C₂²×C₄×C₈	D₁₃	1	1	yes	characteristic
122	C₂×#339	—	13	2	no	—
123	#1729	—	13	2	no	—
124	C₂³×C₁₃	—	2	4	no	—
125	C₂³×C₁₃	#117	1	1	yes	characteristic
126	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
127	C₂³×C₁₃	C₄×Q₈	1	1	yes	characteristic
128	C₂³×C₁₃	#121	1	1	yes	characteristic
129	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
130	C₂³×C₁₃	#124	1	1	yes	characteristic
131	C₂³×C₁₃	#125	1	1	yes	characteristic
132	C₂×C₄×C₁₃	—	2	8	no	—
133	C₂×C₄×C₁₃	—	2	8	no	—
134	C₂×C₄×C₁₃	—	2	8	no	—
135	C₂×C₄×C₁₃	—	2	4	no	—
136	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
137	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
146	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
147	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
148	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
149	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
150	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
151	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
152	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
153	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
154	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
155	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
156	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
157	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
158	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
159	C₂×C₄×C₁₃	#125	1	1	yes	characteristic
160	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
161	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
162	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
163	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
164	C₂×Dic₁₃	—	4	4	no	—
165	C₂×Dic₁₃	—	4	8	no	—
166	C₈×C₁₃	—	2	4	no	—
167	C₈×C₁₃	#95	1	4	yes	—
168	C₈×C₁₃	#95	1	4	yes	—
169	#1055	—	4	4	no	—
170	C₂²×M₁₆	—	13	2	no	—
171	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
172	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
173	C₂×#117	—	13	2	no	—
174	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
175	C₂×#108	—	13	4	no	—
176	C₂×#108	—	26	2	no	—
177	C₂×#108	—	26	2	no	—
178	#427	—	26	2	no	—
179	#427	—	26	2	no	—
180	C₂×#107	—	13	2	no	—
181	C₂×#106	—	13	2	no	—
182	C₂×C₄×C₈	—	2	2	no	—
183	C₂×C₄×C₈	—	2	2	no	—
184	C₂×C₄×C₈	Dic₁₃	1	4	yes	complemented
185	#339	—	26	4	no	—
186	#336	—	26	4	no	—
187	C₂²×C₁₃	—	2	2	no	—
188	C₂²×C₁₃	—	2	2	no	—
189	C₂²×C₁₃	—	2	2	no	—
190	C₂²×C₁₃	—	2	2	no	—
191	C₂²×C₁₃	—	2	2	no	—
192	C₂²×C₁₃	—	2	2	no	—
193	C₂²×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
194	C₂²×C₁₃	#380	1	1	yes	characteristic
195	C₂²×C₁₃	#382	1	1	yes	characteristic
196	C₂²×C₁₃	#389	1	1	yes	characteristic
197	C₂²×C₁₃	#389	1	1	yes	characteristic
198	C₂²×C₁₃	#390	1	1	yes	characteristic
199	C₂²×C₁₃	#391	1	1	yes	characteristic
200	C₂²×C₁₃	#443	1	4	yes	—
201	C₄×C₁₃	—	2	8	no	—
202	C₄×C₁₃	C₂×#95	1	1	yes	characteristic
203	C₄×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
204	C₄×C₁₃	#380	1	1	yes	characteristic
205	C₄×C₁₃	#384	1	1	yes	characteristic
206	C₄×C₁₃	#389	1	1	yes	characteristic
207	C₄×C₁₃	#389	1	1	yes	characteristic
208	C₄×C₁₃	#390	1	1	yes	characteristic
209	C₄×C₁₃	#391	1	1	yes	characteristic
210	Dic₁₃	—	8	4	no	—
211	C₂³×C₄	—	2	1	no	—
212	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
213	C₂×M₁₆	—	13	4	no	—
214	C₂×M₁₆	—	26	2	no	—
215	C₂×M₁₆	—	26	2	no	—
216	C₂×M₁₆	—	26	2	no	—
217	C₂×M₁₆	—	26	2	no	—
218	C₂×M₁₆	—	26	2	no	—
219	C₂²×C₈	—	2	1	no	—
220	C₂²×C₈	—	2	1	no	—
221	C₂²×C₈	—	2	1	no	—
222	C₂²×C₈	—	2	1	no	—
223	C₂²×C₈	—	26	2	no	—
224	C₂²×C₈	Dic₂₆	1	2	yes	—
225	C₂²×C₈	Dic₂₆	1	2	yes	—
226	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
227	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
228	C₂²×C₈	C₄×D₁₃	1	2	yes	—
229	C₂²×C₈	D₅₂	1	2	yes	—
230	C₂²×C₈	D₅₂	1	2	yes	—
231	C₂²×C₈	C₂×Dic₁₃	1	2	yes	—
232	C₂²×C₈	C₂×Dic₁₃	1	2	yes	—
233	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
234	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
235	#117	—	26	2	no	—
236	#117	—	26	2	no	—
237	#117	—	26	2	no	—
238	#117	—	26	2	no	—
239	C₂×C₄⋊C₄	—	13	4	no	—
240	C₂×C₂²⋊C₄	—	26	2	no	—
241	C₂×C₄²	—	2	1	no	—
242	C₂×C₄²	—	2	1	no	—
243	C₂×C₄²	—	2	1	no	—
244	C₂×C₄²	—	26	2	no	—
245	C₂×C₄²	Dic₂₆	1	2	yes	—
246	C₂×C₄²	D₅₂	1	2	yes	—
247	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
248	#108	—	26	8	no	—
249	#107	—	26	4	no	—
250	#106	—	26	4	no	—
251	C₄×C₈	—	2	8	no	—
252	C₂×C₁₃	—	2	1	no	—
253	C₂×C₁₃	—	2	1	no	—
254	C₂×C₁₃	—	2	1	no	—
255	C₂×C₁₃	—	2	1	no	—
256	C₂×C₁₃	C₄⋊#95	1	1	yes	characteristic
257	C₂×C₁₃	#1772	1	2	yes	—
258	C₂×C₁₃	#1945	1	2	yes	—
259	C₂×C₁₃	#1974	1	2	yes	—
260	C₂⁴	#6127	1	1	yes	characteristic
261	C₂²×C₄	—	2	8	no	—
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	26	4	no	—
266	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
267	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
268	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
269	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
270	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
271	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
272	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
273	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
274	C₂²×C₄	#6127	1	1	yes	characteristic
275	C₂²×C₄	#6127	1	1	yes	characteristic
276	C₂²×C₄	#6127	1	1	yes	characteristic
277	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
278	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
279	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
280	M₁₆	—	26	4	no	—
281	M₁₆	—	26	4	no	—
282	M₁₆	—	52	2	no	—
283	M₁₆	—	52	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	26	4	no	—
291	C₂×C₈	—	52	2	no	—
292	C₂×C₈	—	52	2	no	—
293	C₂×C₈	C₄×Dic₁₃	1	2	yes	—
294	C₂×C₈	C₄×Dic₁₃	1	2	yes	—
295	C₂×C₈	#6101	1	2	yes	—
296	C₂×C₈	#6101	1	2	yes	—
297	C₂×C₈	#6101	1	4	yes	—
298	C₂×C₈	C₄⋊Dic₁₃	1	4	yes	—
299	C₂×C₈	C₄⋊Dic₁₃	1	4	yes	—
300	C₂×C₈	#6103	1	2	yes	—
301	C₂×C₈	#6103	1	2	yes	—
302	C₂×C₈	#6103	1	4	yes	—
303	C₂×C₈	C₂²⋊Dic₁₃	1	4	yes	—
304	C₄⋊C₄	—	26	4	no	—
305	C₄⋊C₄	—	26	4	no	—
306	C₂²⋊C₄	—	52	2	no	—
307	C₂²⋊C₄	—	52	2	no	—
308	C₄²	—	2	2	no	—
309	C₄²	—	2	2	no	—
310	C₄²	—	2	2	no	—
311	C₄²	—	52	2	no	—
312	C₄²	—	52	2	no	—
313	C₄²	C₄⋊Dic₁₃	1	4	yes	—
314	C₁₃	#10859	1	1	yes	characteristic, complemented, Sylow
315	C₂³	—	2	4	no	—
316	C₂³	C₄×Dic₂₆	1	1	yes	characteristic
317	C₂³	#88124	1	1	yes	characteristic
318	C₂³	C₄×D₅₂	1	1	yes	characteristic
319	C₂³	#88129	1	1	yes	characteristic
320	C₂³	#88178	1	1	yes	characteristic
321	C₂³	#88180	1	1	yes	characteristic
322	C₂³	#88184	1	1	yes	characteristic
323	C₂×C₄	—	2	8	no	—
324	C₂×C₄	—	2	8	no	—
325	C₂×C₄	—	2	8	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	52	4	no	—
328	C₂×C₄	—	52	8	no	—
329	C₂×C₄	C₄×Dic₂₆	1	1	yes	characteristic
330	C₂×C₄	C₄×Dic₂₆	1	1	yes	characteristic
331	C₂×C₄	C₄×Dic₂₆	1	1	yes	characteristic
332	C₂×C₄	#88123	1	1	yes	characteristic
333	C₂×C₄	#88123	1	1	yes	characteristic
334	C₂×C₄	#88123	1	1	yes	characteristic
335	C₂×C₄	#88124	1	1	yes	characteristic
336	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
337	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
338	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
339	C₂×C₄	#88128	1	1	yes	characteristic
340	C₂×C₄	#88129	1	1	yes	characteristic
341	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
342	C₂×C₄	C₂×#6101	1	1	yes	characteristic
343	C₂×C₄	C₂×#6101	1	1	yes	characteristic
344	C₂×C₄	#88178	1	1	yes	characteristic
345	C₂×C₄	#88178	1	1	yes	characteristic
346	C₂×C₄	#88178	1	1	yes	characteristic
347	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
348	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
349	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
350	C₂×C₄	#88180	1	1	yes	characteristic
351	C₂×C₄	C₂×#6103	1	1	yes	characteristic
352	C₂×C₄	C₂×#6103	1	1	yes	characteristic
353	C₂×C₄	#88184	1	1	yes	characteristic
354	C₂×C₄	#88184	1	1	yes	characteristic
355	C₂×C₄	#88184	1	1	yes	characteristic
356	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
357	C₈	—	2	4	no	—
358	C₈	—	52	4	no	—
359	C₈	#88071	1	4	yes	—
360	C₈	#88071	1	4	yes	—
361	C₂²	—	2	2	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	#11718361	1	4	yes	—
368	C₂²	#11718589	1	1	yes	characteristic
369	C₂²	#11718589	1	1	yes	characteristic
370	C₂²	#11718590	1	1	yes	characteristic
371	C₂²	C₄×C₄⋊Dic₁₃	1	1	yes	characteristic
372	C₂²	#11718597	1	1	yes	characteristic
373	C₂²	#11718600	1	1	yes	characteristic
374	C₂²	#11718873	1	1	yes	characteristic
375	C₄	—	2	8	no	—
376	C₄	—	104	4	no	—
377	C₄	#11718589	1	1	yes	characteristic
378	C₄	#11718589	1	1	yes	characteristic
379	C₄	#11718590	1	1	yes	characteristic
380	C₄	C₄×C₄⋊Dic₁₃	1	1	yes	characteristic
381	C₄	#11718596	1	1	yes	characteristic
382	C₄	#11718600	1	1	yes	characteristic
383	C₄	C₂×#88071	1	1	yes	characteristic
384	C₄	#11718873	1	1	yes	characteristic
385	C₂	—	2	1	no	—
386	C₂	—	2	1	no	—
387	C₂	—	2	1	no	—
388	C₂	—	2	1	no	—
389	C₂	#13113066	1	1	yes	characteristic
390	C₂	#13114715	1	2	yes	—
391	C₂	#13115584	1	2	yes	—
392	C₂	#13115724	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×D₅₂
commutator	C₂×C₄×C₁₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₃
Fitting	C₂²×C₄×C₈×C₁₃	C₂
socle	C₂³×C₁₃	C₄×D₄
prime radical	C₂⁴×C₁₃	#41
cosocle	C₂³×C₄×C₁₃	C₂³
hypercenter	C₂²×C₄×C₈	D₁₃
hypocenter	C₁₃	#10859
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₈ ◁ C₂²×C₄×C₈

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
13. C₂×C₄×C₈×C₁₃	C₄	semidirect
16. C₂×#88059	C₄	semidirect
19. C₂×#88058	C₄	semidirect
20. C₂×#88057	C₄	semidirect
184. C₂×C₄×C₈	Dic₁₃	semidirect
314. C₁₃	#10859	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×#88059	2
C₂×#11718767	2
C₂×#11718115	2
#13114532	2
C₂²×C₄×C₈×C₁₃	2
#10859	13